Synergistic two-variable data assimilation for enhanced turbine blade film-cooling predictions

Data assimilation has been widely employed to enhance the predictive capability of turbulence models, demonstrating significant potential especially in complex flow fields where experimental data are scarce or costly to obtain. In engineering applications such as film cooling of turbine blade, the Reynolds-Averaged Navier–Stokes (RANS) model is commonly adopted due to the relatively low computational cost and practicality for engineering use; however, its predictive accuracy is limited by model simplifications and inherent assumptions, leading to large errors in both wall temperature and heat transfer coefficient. This work proposes a two-variable Ensemble Kalman Inversion (EKI) framework which jointly incorporates wall temperature and heat transfer coefficient as observational constraints, where the weights of error of the two variables are iteratively adjusted. The results show that a faster convergence can be reached compared to the single-variable method, owing to the adaptive assimilation strategy. The relative errors of the predicted wall temperature and heat transfer coefficient are reduced by 68.1% and 75.9%, respectively, compared to the baseline RANS model. Furthermore, for the generation of ensemble members, a spatially smooth continuous perturbation method is proposed to avoid non-physical solutions, thereby significantly reducing the amount of experimental data needed across different operating conditions.